Blackbody radiation and the Ultraviolet Catastrophe

[Jimmy87]

Hi, please could someone help me as I am struggling to understand the classical blackbody theory. I will briefly summarize what my textbook says. It says that if the classical model was correct then a tennis ball should be emitting radiation in mainly the ultraviolet region. The idea at the time was that atoms in the blackbody were thought of as oscillators which could vibrate at any frequency. The higher frequency oscillations would have more modes thus more ways of storing energy and therefore one would expect to find most of the energy in the ultraviolet range for any object above absolute zero as this is where most of the modes are. What I am struggling to understand is how this classical theory applies to low temperature objects such as a tennis ball. Even if the atoms of a tennis ball do indeed have more modes for the higher frequency oscillators where would it get the energy from to fill these modes when its only at room temperature!? I can see the logic (even though its wrong) that increasing the temperature/intensity would increase the radiation emitted all the way up to infinity but how does this classical theory also mean that things at room temperate for example, should also emit in mainly the ultraviolet region? Any help would be greatly appreciated!

 

[Bill_K]

Even if the atoms of a tennis ball do indeed have more modes for the higher frequency oscillators where would it get the energy from to fill these modes when its only at room temperature!?

Well sure, that's exactly the problem with the classical theory, isn't it?

Thus, both the power at a given frequency and the total radiated power is unlimited as higher and higher frequencies are considered: this is clearly unphysical as the total radiated power of a cavity is not observed to be infinite,

 

[Jimmy87]

Well sure, that's exactly the problem with the classical theory, isn't it?

Yes, but I'm saying that if we pretend the classical view was correct (and quantum mechanics didn't exist) where would a tennis ball get the energy from to radiate in the UV range as this is what the theory apparently predicted (Lord Rayleigh predicted this) but I don't see how. So even though its wrong I don't understand how Rayleigh predicted objects with room temperature should emit mostly in the UV range.

 

[Bill_K]

Rayleigh attempted to calculate the black body spectrum. The result he got was only partially successful. It worked for low frequencies and failed at high frequencies. He was well aware of this. He never pretended it was correct.

 

[Jano L.]

where would it get the energy from to fill these modes when its only at room temperature!?

The Rayleigh calculation seems to give good result for intensity of low frequency component of the radiation. The energy corresponding to this radiation comes from the other objects used to heat the tennis ball up to its temperature.

If we attempt to extend the validity of the Rayleigh calculation to higher frequencies, mathematically we can, and the energy would again come from the surrounding objects. But what Bill is saying is right, for high frequencies the assumptions of the calculation are implausible and the result experimentally fails.

 

[Jimmy87]

Thanks for all your answers guys, that has helped